A Levenberg–Marquardt Method for Solving the Tensor Split Feasibility Problem

This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈Q.If we simply take this problem as a special case of the nonlinear split feasibility problem,then we can directly get a projection method to solve it.However,applying this kind of projection method to solve the tensor split feasibility problem is not so efficient.So we propose a Levenberg–Marquardt method to achieve higher efficiency.Theoretical analyses are conducted,and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method.